\documentclass[12pt]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% DSM 2010.02.08
\usepackage{amsfonts, bm, amsmath, color, natbib, rotating, amsthm, subfigure, lscape, multicol, epstopdf, verbatim} 


%% THE NEXT TWO LINES INSERT THE PACKAGES FOR JASA FORMAT:
%\usepackage[default]{jasa_harvard}    % 	for formatting citations in text
\usepackage{/Latex/JASA_manu}
\bibpunct{(}{)}{;}{a}{}{,}

%% CHANGING THE 'AND' IN THE HARVARD BIBLIOGRAPHY PACKAGE TO WHAT IT OUGHT TO BE
%\renewcommand{\harvardand}{and}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setlength{\oddsidemargin}{-0.125in}
\setlength{\topmargin}{-0.5in}
\setlength{\textwidth}{6.5in}
\setlength{\textheight}{9in}

\setlength{\textheight}{9in}
\setlength{\textwidth}{6.5in}
\setlength{\topmargin}{-40pt}
\setlength{\oddsidemargin}{0pt}
\setlength{\evensidemargin}{0pt}

\setlength{\textheight}{9in}
\setlength{\textwidth}{6.5in}
\setlength{\topmargin}{-36pt}
\setlength{\oddsidemargin}{0pt}
\setlength{\evensidemargin}{0pt}
\tolerance=500
\renewcommand{\baselinestretch}{1.5}
\input /Latex/psfig.tex

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\rjccomment#1{\vskip 2mm\boxit{\vskip 2mm{\color{red}\bf#1} {\color{blue}\bf -- RJC\vskip 2mm}}\vskip 2mm}
\def\wt{\widetilde}
\def\diag{\hbox{diag}}
\def\wh{\widehat}
\def\AIC{\hbox{AIC}}
\def\BIC{\hbox{BIC}}
\def\diag{\hbox{diag}}
\def\log{\hbox{log}}
\def\bias{\hbox{bias}}
\def\Siuu{\boldSigma_{i,uu}}
\def\dfrac#1#2{{\displaystyle{#1\over#2}}}
\def\VS{{\vskip 3mm\noindent}}
\def\boxit#1{\vbox{\hrule\hbox{\vrule\kern6pt
          \vbox{\kern6pt#1\kern6pt}\kern6pt\vrule}\hrule}}
\def\refhg{\hangindent=20pt\hangafter=1}
\def\refmark{\par\vskip 2mm\noindent\refhg}
\def\naive{\hbox{naive}}
\def\itemitem{\par\indent \hangindent2\parindent \textindent}
\def\var{\hbox{var}}
\def\cov{\hbox{cov}}
\def\corr{\hbox{corr}}
\def\trace{\hbox{trace}}
\def\refhg{\hangindent=20pt\hangafter=1}
\def\refmark{\par\vskip 2mm\noindent\refhg}
\def\Normal{\hbox{Normal}}
\def\povr{\buildrel p\over\longrightarrow}
\def\ccdot{{\bullet}}
\def\bse{\begin{eqnarray*}}
\def\ese{\end{eqnarray*}}
\def\be{\begin{eqnarray}}
\def\ee{\end{eqnarray}}
\def\bq{\begin{equation}}
\def\eq{\end{equation}}
\def\bse{\begin{eqnarray*}}
\def\ese{\end{eqnarray*}}
\def\pr{\hbox{pr}}
\def\wh{\widehat}
\def\trans{^{\rm T}}
\def\myalpha{{\cal A}}
\def\th{^{th}}
\long\def\symbolfootnote[#1]#2{\begingroup%
\def\thefootnote{\fnsymbol{footnote}}\footnote[#1]{#2}\endgroup}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% DSM 2010.10.01
\def\mathbi#1{\textbf{\em #1}}
\newcommand{\utwi}[1]{\mbox{\boldmath $ #1$}}

\newcommand{\bx}{{\utwi{x}}}
\newcommand{\by}{{\utwi{y}}}
\newcommand{\bz}{{\utwi{z}}}

\newcommand{\balpha}{\utwi{\alpha}}
\newcommand{\bbeta}{\utwi{\beta}}
\newcommand{\bvarepsilon}{\utwi{\varepsilon}}



\newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}} 
\def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}
\newcommand{\argmin}{\operatornamewithlimits{argmin}}

\newtheorem{thm}{\normalfont{Theorem}}[section]
\newtheorem{asm}[thm]{\normalfont{Assumption}}
\newtheorem{lem}[thm]{\normalfont{Lemma}}
\newtheorem{cor}[thm]{\normalfont{Corollary}}
%\newcommand{\qed}{\hfill \ensuremath{\Box}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\thispagestyle{empty}
\baselineskip=28pt %28pt

\begin{center}
{\LARGE{\bf TITLE}} 
\end{center}

\baselineskip=20pt 
\vskip 5mm
\begin{center}
David S. Matteson and Timothy D. Roberts
\symbolfootnote[0]{\baselineskip=10pt 
Matteson is Visiting Assistant Professor, 
School of Operations Research and Information Engineering,
Cornell University,
282 Rhodes Hall,
Ithaca, NY 14853
(E-mail: {\it dm484@cornell.edu}).
Roberts is ...
(E-mail: {\it timothy.daniel.roberts@gmail.com}).}  
\vskip 5mm
\today
\end{center}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\clearpage\pagebreak\newpage
%\thispagestyle{empty}
\begin{center}
{{ABSTRACT}}
\end{center}
\baselineskip=18pt

...

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\baselineskip=18pt
\par\vfill\noindent
{\bf KEY WORDS:}
Dimension Reduction;
Principal Component Analysis.
\par\medskip\noindent
{\bf Short title: ...}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage\pagebreak\newpage
\pagenumbering{arabic}
\section{Introduction} \label{sec:seca}
\newlength{\gnat}
\setlength{\gnat}{24pt} %{24pt} double %{18pt} 1.5 % {12pt} single space
\baselineskip=\gnat


Dimension reduction method (Factor models)


Let $\bx_t = (\bx_{1t}, \bx_{2t})$ and run the following regressions:

$\by_t = \balpha \bx_{1t} + \bvarepsilon_{1,t}$

$\bx_{2t} = \bbeta \bx_{1t} + \bvarepsilon_{2,t}$

Conditional on $\bx_{1}$, is $\by \independent \bx_{2}$?

Test $\bvarepsilon_{1,t} \independent \bvarepsilon_{2,t}$

Note, $\bvarepsilon_{1,t}, \bvarepsilon_{2,t}$ may each be serially dependent. 

Three applications come to mind:

\begin{enumerate}
\item This can be a regular multivariate regression. Run your favorite model selection algorithm, is your favorite subset adequate?

\item Principal component analysis. Let $\bx_{1}$ be the first few PCs from $\by$. Are they adequate?


\item I think this can also be formulated as a Granger causality test, let $\bx$ be lagged values of $\by$

\end{enumerate}


Some simulations:

Generate $(\bx_{1t}, \bx_{2t})$ as multivariate Normal/T with varying levels of correlation. T may still have tail dependence at cor = 0.

Let 

\begin{equation}\label{eq1}
\by_t = \bx_{1t} + \bx_{2t} + \bvarepsilon_{3,t}
\end{equation}

and run test. Equation (\ref{eq1})

\subsection{subsection}

\cite{szekely2009brownian}

\cite{szekely2007measuring}

\cite{energy}

\cite{remillard2009discussion}

\section{Conclusion}

This is great, publish us!


\baselineskip=12pt


%\section*{Supplemental Materials}
%\begin{description}

%\item[Technical Arguments:] ..... (SupplementalMaterials.pdf)
%\end{description}

%\bibliographystyle{abbrv}


\bibliographystyle{/Latex/jasa} %{Chicago} %{ECA_jasa}
\baselineskip=12pt
%\vspace{-0.9cm}
\bibliography{/Latex/Matteson_ICA}




\end{document}


% in R: 
%          setEPS(horizontal = FALSE, onefile = FALSE, paper = "special")
% then use postscript()


\clearpage\pagebreak\newpage
\thispagestyle{empty}

\begin{landscape}

\begin{figure}
\begin{minipage}[b]{0.5\linewidth} % A minipage that covers half the page
\centering
\includegraphics[width = 4.5in, height = 5.4in]{figures/gdpLoadingsNew}
\caption{
\baselineskip=10pt
The loadings on pairs of factors for the United States (US), Canada (CA), United Kingdom (UK), Korea (KO), and Taiwan (TW) for selected components: (a) Loadings on the first two PCs; (b) Loading from the FastICA method restricted to only the first two PCs; (c) Loading on the first two ICs from the FastICA method via a deflation algorithm; (d) Loading on two DOCs selected from our generalized decorrelation method.
}
\label{gdpFit}
\end{minipage}
\hspace{0.5cm} % To get a little bit of space between the figures
\begin{minipage}[b]{0.5\linewidth}
\centering
\includegraphics[width = 4.5in, height = 6
in]{figures/analysis_plot_1.pdf}
\caption{
\baselineskip=10pt
Daily log returns, in percentages, of (a) the S\&P 500 Index, (b) Cisco Systems stock, and (c) Intel Corporation stock from January 2, 1991 to December 31, 1999.}
\label{fig:anal_1}
\end{minipage}
\end{figure}

\end{landscape}


\clearpage\pagebreak\newpage
\thispagestyle{empty}



\begin{table}
\caption{\label{tbl-sci} Summary statistics for S\&P 500 Index, Cisco, and Intel stock's daily percentage log returns from January 2, 1991 to December 31, 1999 considered in Section \ref{app2}.}
\begin{center}
{\footnotesize %\scriptsize 
\begin{tabular}{|cc|rrrc|} 
\hline
& & S\&P 500 & Cisco & Intel & \\
 \hline
& Mean               & 0.066   & 0.257  & 0.156 & \\
& Standard Deviation & 0.875   & 2.854  & 2.464 & \\
& Minimum            &-7.114   &-22.100 &-14.581 & \\
& Maximum            & 4.990   & 15.576 & 12.850 & \\
& Skewness           &-0.360   &-0.396  &-0.235  & \\
& Excess Kurtosis    & 6.039   & 3.717  & 2.465   &\\
\hline
\end{tabular} }
\end{center}
\end{table} 


\end{document}
